Question

2a) solve the equation $3(x + 9)^2 - 15 = 0$ by inverse operations.

Explanation:

Step1: Add 15 to both sides

To isolate the term with the square, we add 15 to both sides of the equation \(3(x + 9)^2 - 15 = 0\). This gives us \(3(x + 9)^2 = 15\).

Step2: Divide both sides by 3

Next, we divide both sides by 3 to further isolate the squared term. So, \((x + 9)^2=\frac{15}{3}=5\).

Step3: Take square root of both sides

Taking the square root of both sides, we get \(x + 9=\pm\sqrt{5}\).

Step4: Subtract 9 from both sides

Finally, we subtract 9 from both sides to solve for \(x\). This gives us \(x=-9\pm\sqrt{5}\).

Answer:

\(x = -9 + \sqrt{5}\) or \(x = -9 - \sqrt{5}\)